A review of some methods for ranking fuzzy subsets.

*(English)*Zbl 0567.90056The paper consists of two parts. In the first part the authors review methods for ranking n fuzzy subsets of a number space (fuzzy numbers) well-known in the literature. This review takes into account almost all methods which have been elaborated till now. In the second part the authors report on testing these methods, giving twenty numerical examples. In these examples different forms of the membership functions of the ranked fuzzy subsets are included. This part of the paper seems to be controversial. Obviously it may be interesting for the reader how the methods formally behave in situations presented in the examples. However an ascertainment of anyting on the quality (correctness) of these methods on the basis of such an analysis seems to be controversial and risky and may lead the reader into error, because in different situations fuzzy subsets may be interpreted in a different manner and their membership functions may be variously determined. There are no established and generally obligatory rules in this respect - and this fact must be taken into account during the quality analysis of the methods.

Reviewer: S.Chanas

##### MSC:

90B50 | Management decision making, including multiple objectives |

91B08 | Individual preferences |

03E72 | Theory of fuzzy sets, etc. |

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\textit{G. Bortolan} and \textit{R. Degani}, Fuzzy Sets Syst. 15, 1--19 (1985; Zbl 0567.90056)

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